2 Need for using a FE modelA wind turbine tower is a simple cantilever.Assuming uniform wind pressure along its height, moment & shear force at any point can be calculated directly regardless of the tower configurationEven when tower wind pressure is a function of height[ p=p(h) ] , moment & shear at the base can be calculated also by simple integrations of the load functionHISTWIN-High strength steel tower for wind turbines - RFSR-CT

3 Need for using a FE modelMeridional stress for local buckling check can also be easily calculated by handTower displacements & eigenmodes can’t be calculated so easily because of the change of the elastic characteristics of the cantilever along its height.For this calculation a computational model is neededHISTWIN-High strength steel tower for wind turbines - RFSR-CT

4 Need for using a FE modelComputational model (Linear):All sections of the tower are simulated via linear beam elements.Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricitySoil-structure interaction can be simulated by the use of a rotational spring at tower baseBy the use of a linear model we can calculate tower displacements and perform an eigenvalue analysis with accurate results.So what’s the need for a Finite Element model?HISTWIN-High strength steel tower for wind turbines - RFSR-CT

5 Need for using a FE modelCross section of the tower is deformed due to the wind loadsStress concentration at the door position cannot be estimated by a linear modelBolt forces at flange positions cannot be calculated from the linear model. A special FE model is needed.Anchor forces and the stress state of theconcrete on anchoring position need to be determined.Soil-structure interaction affects the tower dynamic characteristics, and its displacements for wind loading.HISTWIN-High strength steel tower for wind turbines - RFSR-CT

6 Need for using a FE modelWind pressure distribution over the circumference of the tower causes ovalling of the circular tower sectionBut when it comes to the positions where the tower section is much stiffer (flange & support positions) , the section shape is forced to be circular.This causes circumferencial stresses to the shell near flange positionsIn buckling check (EC 3-1-6) not only meridional stress but circumferencial & shear stresses are used in combination as wellHISTWIN-High strength steel tower for wind turbines - RFSR-CT

7 Modern Finite Element SoftwareA few years ago, developing of a complex Finite Element modelwas very difficult due to:Need of expensive big computers (and expensive software) to run a non-linear analysisToo much effort for developing the FE model geometry and loadingToο much effort by hand to interpret the results (stress integrations etc).Modern Finite Element software that can run on a simple PC offer:Direct input of the geometry from CAD softwareCAD capabilities inside the FEM softwareGeometrical & material non-linear analysis capabilitiesUnilateral contact with friction capabilitiesNon-linear analysis now can run on a personal computerAutomatic procedures for results interpretationInterfaces to join with design softwareHISTWIN-High strength steel tower for wind turbines - RFSR-CT

8 Modelling Strategies can be described by the chart below:Overall modelLinearFE modelFoundationFoundation includedSeparate model for the FoundationFoundation modelLinear (grid on elastic support)FE model (including anchoring detail)Details (Flanges, Door position etc) : Finite ElementsSeparate models for the detailsIncluded to the general modelThree different strategies will be presentedHISTWIN-High strength steel tower for wind turbines - RFSR-CT

12 Modelling strategies – 1:Linear modelAdvantages:Easy developing of the general model and the part modelsFast calculation (on a simple PC: instant calculation for the overall model & minutes for the non-linear models of the flanges)Easy change of the model configurationDisadvantages:Circumferencial variation of the tower loads cannot be introducedBoundary conditions for the part models need to be estimatedOnly meridional stress can be calculatedCircumferencial & shear stresses are neglectedEC requires the complete stress-state (meridional, circumferencial & shear) for the buckling checkOnly Axial & Shear forces and Bending moment are available to be applied to the part models. In- plane deformation of the tower due to the wind load distribution is neglectedSoil-structure interaction is neglected or need to be estimated by introducing a rotational spring on tower supportHISTWIN-High strength steel tower for wind turbines - RFSR-CT

13 Modelling strategies – 1:Linear modelModelling the foundation by linear elements(grid of beams on unilateral elastic support)to simulate soil-structure interactionSimulates soil-structure interactionGood for the design of the foundationIt doesn’t give an answer to the stress state of the anchoring systemHISTWIN-High strength steel tower for wind turbines - RFSR-CT

15 Modelling strategies - 2:Simple FE modelAdvantages:Fast calculation in PC (about 1-2 minutes a run for the general model and about minutes for the non-linear analysis of the flange models)Estimation of the full stress-state on any pointDisadvantages:Boundary conditions for the part models need to be estimatedMuch effort is needed for the transfer by hand the stress-state of a specific cross-section to the corresponding cross-section of the part model.Soil-structure interaction is neglected or need to be estimated by introducing springs on tower supportHISTWIN-High strength steel tower for wind turbines - RFSR-CT

25 Modelling strategies - 3:Detailed FE modelAdvantages:Estimation of the full stress-state on any pointBest possible approximation to the real-world situationNo transfer of loads is needed from one model to anotherNo need to estimate any partial model boundary conditionsDisadvantages:Big effort for developing the FE modelChanges to the model are difficultNon-linear calculation needs time to run on a personal computer (can take 4-5 hours a run on a modern PC)HISTWIN-High strength steel tower for wind turbines - RFSR-CT

26 Tower loads Vertical loadsSelf mass & weight is estimated directly by the FE softwareThe rotor & nacelle mass is applied to the top of the tower distributed to the nodes ofthe upper flange taking into account the eccentricity(mass instead of loads, to be used in spectrum analysis as well)‏Wind loadsAt the top of the tower, rotor forces and moments areappliedAt tower stem wind pressure is calculatedacc. EC1-1-4 as a logarithmic function of z.HISTWIN-High strength steel tower for wind turbines - RFSR-CT

28 Types of analysis Seismic loading:Response spectrum analysis for the seismic loading must be performedAdditional time history harmonic response analysis for the seismic loading(only in extreme cases)‏Due to the distributed mass of the tower itself two eigenmodes are participating. Equivalent lateral load method cannot be usedHISTWIN-High strength steel tower for wind turbines - RFSR-CT

31 Comparison of the results for the three modelsComparison of resultsComparison of the results for the three modelsHISTWIN-High strength steel tower for wind turbines - RFSR-CT

32 Conclusions:Although the use of an overall complex Finite Element model needs more calculation effort, it is necesary in order to establish a better approach the stress state on the structureWith modern Finite Element software such a nonlinear analysis can be run on a simple personal computerThe cost of developing such a model is extremely small compared with the budget of a single aeolic park installationSimplified models (linear model, even hand-calculation) are also necessary to develop in paralell, for initial design, and for checking the results of the FE modelHISTWIN-High strength steel tower for wind turbines - RFSR-CT